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Inverse problems for locally perturbed lattices -- Discrete Hamiltonian and quantum graph

Mathematical Physics 2022-02-03 v1 math.MP Spectral Theory

Abstract

We consider the inverse scattering problems for two types of Schr\"odinger operators on locally perturbed periodic lattices. For the discrete Hamiltonian, the knowledge of the S-matrix for all energies determines the graph structure and the coefficients of the Hamiltonian. For locally perturbed equilateral metric graphs, the knowledge of the S-matrix for all energies determines the graph structure.

Keywords

Cite

@article{arxiv.2202.00944,
  title  = {Inverse problems for locally perturbed lattices -- Discrete Hamiltonian and quantum graph},
  author = {Emilia Blåsten and Pavel Exner and Hiroshi Isozaki and Matti Lassas and Jinpeng Lu},
  journal= {arXiv preprint arXiv:2202.00944},
  year   = {2022}
}

Comments

36 pages, 4 figures